Groupings and Pairings in Anonymous Networks
Bibliographic record
Abstract
Abstract. We consider a network of processors in the absence of unique identities, and study the k-Grouping problem of partitioning the processors into groups of size k and assigning a distinct identity to each group. The case k = 1 corresponds to the well known problems of leader election and enumeration for which the conditions for solvability are already known. The grouping problem for k ≥ 2 requires to break the symmetry between the processors partially, as opposed to problems like leader election or enumeration where the symmetry must be broken completely (i.e. a node has to be distinguishable from all other nodes). We determine what properties are necessary for solving these problems, characterize the classes of networks where it is possible to solve these problems, and provide a solution protocol for solving them. For the case k = 2 we also consider a stronger version of the problem, called Pairing where each processor must also determine which other processor is in its group. Our results show that the solvable class of networks in this case varies greatly, depending on the type of prior knowledge about the network that is available to the processors. In each case, we characterize the classes of networks where Pairing is solvable and determine the necessary and sufficient conditions for solving the problem. 1
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".